This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A075557 #14 Dec 08 2024 04:00:55 %S A075557 3,5,7,13,37,31,23,17,53,11,251,29,79,43,73,61,97,67,107,173,59,103, %T A075557 199,163,71,149,47,101,509,89,151,283,229,271,211,109,257,113,269,157, %U A075557 241,331,83,389,41,313,1543,19,307,463,373,277,811,457,137,191,419,311,197 %N A075557 a(n) is the smallest odd prime such that (1) a(n) doesn't already appear in the sequence; (2) the n-th partial sum is divisible by n; and (3) the n-th partial sum is relatively prime to n+1. %C A075557 Condition (3) is needed to ensure that a(n+1) exists. %H A075557 Robert Israel, <a href="/A075557/b075557.txt">Table of n, a(n) for n = 1..10000</a> %e A075557 a(5)=37: The 4th partial sum is 28. 7 is the smallest odd prime that satisfies (2) (28+7=35), but 7 has already been used. 17 satisfies (1) and (2) (28+17=45), but 45+a(6) must be a multiple of 6 and the only odd prime satisfying that requirement is 3, which has already been used. 37 works (28+37=65). %p A075557 N:= 10000: # for terms until the first term > N. %p A075557 Cands:= select(isprime, [seq(i,i=3..N,2)]): %p A075557 nC:= nops(Cands): %p A075557 R:= NULL: s:= 0: %p A075557 for n from 1 do %p A075557 found:= false; %p A075557 for i from 1 to nC do %p A075557 if s + Cands[i] mod n = 0 and igcd(s + Cands[i],n+1) = 1 then %p A075557 R:= R, Cands[i]; %p A075557 s:= s + Cands[i]; %p A075557 Cands:= subsop(i=NULL,Cands); %p A075557 nC:= nC-1; %p A075557 found:= true; %p A075557 break %p A075557 fi %p A075557 od; %p A075557 if not found then break fi %p A075557 od: %p A075557 R; # _Robert Israel_, Dec 07 2024 %Y A075557 Cf. A065091 (odd primes). %K A075557 nonn,easy,look %O A075557 1,1 %A A075557 _Amarnath Murthy_, Sep 24 2002 %E A075557 Edited by _David Wasserman_, Jun 27 2003 %E A075557 Corrected by _Robert Israel_, Dec 07 2024